The company said Friday that it was studying options "to allow broad public participation in its equity," including an IPO of the group or some of its subsidiaries.

Aramco is the world's largest oil producer: It claims to pump 12% of the world's crude oil.

It also sits on a huge amount of oil. It says it has 261 billion barrels of proven reserves, roughly 15% of the world's total.

'Desperate' for cash

The fact that Saudi Arabia is considering selling now, when oil prices have collapsed to their lowest in a decade, speaks volumes about its dire financial situation.

"Saudi Arabia is experiencing uncontrollable and unsustainable spending on defense and subsidies... they are desperate to raise cash," said Luay al-Khatteeb, energy security expert and a fellow at the Brookings Doha Center.

Oil accounts for 75% of Saudi Arabia's revenue, and the plunge in prices is hurting big time.

The government spent way more than it collected in 2015 -- leading to a budget deficit of nearly $100 billion. It has announced a series of spending cuts, and even hiked the price of gasoline by 50%.

Oil hit its lowest level in 12 years earlier this week, having collapsed from well over $100 per barrel to just above $33 in the last 18 months. That means Aramco is also worth much less than it was a few years back.

Still, even a partial stock market listing would raise many billions of dollars.

Bigger than Apple?

The big question is whether an IPO would even be technically possible. Aramco might simply be too big to be listed, at least on the Saudi market.

It could be worth trillions of dollars, according to The Economist, which first reported Aramco may list its shares. That would be more than all Saudi stocks put together, and make it bigger than Apple(AAPL).

By comparison, the world's biggest listed oil company -- Exxon Mobil (XOM)-- has a market capitalization of $314 billion, with about 10% of Aramco's proven reserves.

"The authorities could consider [an] IPO in a part of the company and gradually building it toward capacity as the market increases," said Saudi economist Fahad Al-Turki.

Aramco was founded in the 1930s. Originally called the Arabian American Oil Company, Saudi Aramco became fully state-owned by the late 1970s.

It has discovered more than 100 oilfields in Saudi Arabia and employs about 60,000 people.